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Citation Laibson, David I. 2001. A cue-theory of consumption. QuarterlyJournal of Economics 116(1): 81-119.

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A CUE-THEORY OF CONSUMPTION*

DAVID LAIBSON

Psychological experiments demonstrate that repeated pairings of a cue and aconsumption good eventually create cue-based complementarities: the presence ofthe cue raises the marginal utility derived from consumption. In this paper, suchdynamic preferences are embedded in a rational choice model. Behavior thatarises from this model is characterized by endogenous cue sensitivities, costlycue-management, commitment, and cue-based spikes in impatience. The model isused to understand addictive/habit-forming behaviors and marketing. The modelexplains why preferences change rapidly from moment to moment, why tempta-tions should sometimes be avoided, and how firms package and position goods.

I. INTRODUCTION AND MOTIVATION

The patient was a 28-year-old man with a ten-year history of narcoticaddiction. He was married and the father of two children. He reported that,while he was addicted, he was arrested and incarcerated for six months. Hereported experiencing severe withdrawal during the first four or five days incustody, but later, he began to feel well. He gained weight, felt like a newman, and decided that he was finished with drugs. He thought about hischildren and looked forward to returning to his former job. On the way homeafter his release from prison, he began thinking of drugs and feeling nause-ated. As the subway approached his stop, he began sweating, tearing from hiseyes, and gagging. This was an area where he had frequently experiencednarcotic withdrawal symptoms while trying to acquire drugs. As he got offthe subway, he vomited onto the tracks. He soon bought drugs and wasrelieved. The following day he again experienced craving and withdrawalsymptoms in his neighborhood, and he again relieved the symptoms byinjecting heroin. The cycle repeated itself over the next few days and soon hebecame readdicted [O’Brien 1976, p. 533].

Environmental cues sometimes elicit changes in preferences/behavior. Hence, cues and consumption are sometimes comple-ments: cues raise the marginal utility of consumption. The nar-rative above describes an unusually powerful case of this

* This work has been supported by the National Science Foundation (SBR-9510985) and the MacArthur Foundation. I am particularly grateful to anony-mous referees whose careful comments dramatically improved this paper, to QJEeditors Edward Glaeser and Andrei Shleifer, and to Jeroen Swinkels who drew myattention to the association between cues and motivational states. I have alsobenefited from the insights of Colin Camerer, Peter Diamond, George Loewen-stein, Gregory Mankiw, Drazen Prelec, Paul Romer, Richard Zeckhauser, andseminar participants at Brown University, Columbia University, Cornell Univer-sity, Harvard University, MacArthur Foundation Preferences Group, NationalBureau of Economic Research, and Norwegian Research Council Addiction Group.Meghana Bhatt, Xiaomeng Tong, and Stephen Weinberg provided excellent re-search assistance.

© 2001 by the President and Fellows of Harvard College and the Massachusetts Institute ofTechnology.The Quarterly Journal of Economics, February 2001

81

phenomenon. Few of us ever experience cue-consumption comple-mentarities as potent as those of the heroin addict. However, lessextreme examples are commonplace. Consider cues like the smellof cookies baking, smell of perfume/cologne, sound of ice fallinginto a whiskey tumbler, sight of a bowl of ice cream, and sight ofa pack of cigarettes.

Preferences are sensitive to cues like these, explaining whythose preferences often vary from moment to moment. The sightof a dessert tray at the end of a meal will induce a diner to ordersomething sweet, reversing an earlier resolution to forgo theextra calories. Likewise, the sight of a familiar drug-taking envi-ronment will induce drug craving in an addict, even if the addicthas just completed a six-month detoxification therapy. Cues gen-erate high frequency variation in preferences/cravings, explain-ing apparently random behavior. Cues also play a role in themarketing strategies of firms (e.g., supermarkets create artificialfood smells to stimulate shopper demand and surround checkoutaisles with candy). Moreover, when consumers understand thesemechanisms, consumers try to influence the sequence of cues theyexperience (e.g., recovering alcoholics avoid the smell or sight ofalcohol). Cues serve as an important endogenous variable, whichfirms, consumers, and governments try to control.

This paper argues that cues are an important determinant ofhabit-forming behaviors and that cue effects can be capturedusing minor variants of the models that Becker and Murphy havedeveloped in their papers on rational addiction and advertising[1988, 1993]. The Becker-Murphy rational addiction model as-sumes that past consumption is complementary with currentconsumption, thereby explaining the formation of habits andaddictions. The Becker-Murphy advertising model assumes thatadvertisements (i.e., sensory inputs like cues) are complementarywith consumption, formalizing the role of marketing. The currentpaper draws a connection between these two heretofore distinctforms of complementarity.

The connection is already discussed in the psychology litera-ture. For example, it is known that heroin addicts experience aheightened desire (i.e., marginal utility) for heroin consumptionwhen they experience the cues associated with past use of heroin.Likewise, cigarette smokers experience a heightened nicotinecraving when they see smoking cues, like an open box of ciga-rettes. The cues model in the current paper captures these pat-terns by assuming that habit formation effects are turned on and

82 QUARTERLY JOURNAL OF ECONOMICS

off by the presence or absence of cues (i.e., sensory inputs) thathave been associated with past consumption of habit-forminggoods. Hence, the cues model assumes that a current cue iscomplementary with current consumption if that cue has beenassociated with consumption in the past. For example, if thesound of ice cubes falling into a tumbler has reliably predictedingestion of Scotch in the past, then that sound will elevate thecurrent marginal utility of Scotch (i.e., will increase one’s desirefor a glass of Scotch). Likewise, if the smell of baking cookies hasreliably predicted feeding in the past, then the current smell ofbaking cookies will elevate the current marginal utility of feeding.

This paper documents and explains the existence of such adynamic utility function, using psychological evidence. The paperthen models the choices of a rational decision maker who hascue-contingent habit formation. The decision-maker can manipu-late the dynamic pairing of cues and behavior as well as cue-exposure. The model embeds these preferences in a rationalchoice framework that is closely related to the habit formationmodel of Becker and Murphy [1988], and assumes an underlyingstable meta-utility structure [Becker 1996].

In the body of the paper I highlight four implications of thecues model. First, the model generates multiple steady states,some of which are characterized by cue-contingent marginal util-ity effects (i.e., cue-based drives). In these cue-based steadystates, equilibrium actions vary at high frequency and depend onseemingly arbitrary cues (i.e., white noise that is uncorrelatedwith any other exogenous variable in the consumer’s problem).Second, the cues model predicts that consumers will engage inactive cue-management. Under reasonable parameter specifica-tions, consumers are willing to spend almost all of their income tomanipulate the sequence of cues they experience. Hence, arbi-trary cues have important welfare implications. Third, the modelpredicts that consumers will pay to reduce their own future choiceset, even though the consumers have dynamically consistent pref-erences. This paradoxical commitment arises because in someversions of the model, choice sets are linked one-to-one with cues(you cannot smoke a cigarette without seeing one). Hence, largechoice sets introduce cue-based temptations that are costly toresist. Fourth, links between cues and rewards imply that thepresence of reward opportunities may generate drives that makedelay of gratification difficult. This explains why consumers oftenexhibit extreme impatience over the short run (when the reward

83A CUE-THEORY OF CONSUMPTION

opportunity cue is present), while maintaining a long-run prefer-ence for patience.

The paper is organized as follows. Section II summarizesrelevant psychology research, and then presents a dynamic choicemodel that integrates these findings. In addition, Section II char-acterizes the solution of the model. Section III interprets themodel and formally establishes the results outlined here. SectionIV contrasts the view of habits discussed in this paper with thenow standard model of habits presented in Becker and Murphy[1988]. The new model explains why tastes and cravings changerapidly from moment to moment, why temptations should some-times be actively avoided, how firms position and package goods,and why public consumption generates negative externalities.Section V concludes.

II. PREFERENCES

This section presents a stable meta-utility function [Becker1996]. Its functional form is fixed by nature and is beyond controlof the consumer. The following subsection summarizes psycholog-ical evidence that motivates this functional form.

II.1. Psychological Evidence on Preference Dynamics

Classical conditioning experiments pair a behaviorally neu-tral cue—e.g., bells in Pavlov’s [1904] dog experiment—with abehaviorally nonneutral stimulus—e.g., a feeding opportunity. InPavlov’s experiment the food elicits salivation. Repeated pairingsof the bells and the food eventually lead the bells to generate thesame salivatory response that was originally generated by thefeeding. Ringing the bells elicits salivation whether or not the bellis followed by a feeding session. Psychologists call cue-elicitedbehavior “conditioned responses.” Many (but not all) conditionedresponses are physiologically preparatory; e.g., for Pavlov’s dogs,salivation prepares the organism for food ingestion. Such prepa-ratory responses are generally evolutionarily adaptive. The or-ganism’s fitness is improved by cue-triggered preparatory mech-anisms that are based on past associations between cues (theringing bells) and behavior (feeding).1

Dozens of studies document the existence of such automatic

1. This paper explores the role of preparatory conditioned responses. For adiscussion about the scope of preparatory conditioning phenomena, see Solomon


physiological mechanisms.2 For example, exposure to food cues(e.g., visual, oral, spatial, or temporal) initiates a host of special-ized digestive processes: salivary, gastric, pancreatic exocrine,pancreatic endocrine (insulin), thermogenic, and cardiovascular.3Analog preparatory mechanisms are initiated when organismsare exposed to familiar drug cues. Many of these preparatorymechanisms are physiologically compensatory in the sense thatthey compensate for or offset the effect of the drug. For example,rats that have repeatedly received anaesthetizing morphine in-jections in the presence of a particular cue eventually develop anincreased responsiveness to pain (hypersensitivity) in the pres-ence of that cue.4 This cue-conditioned hypersensitivity partiallyoffsets the anaesthetic effect that will be generated if the rat issubsequently injected with morphine. Offsetting the morphine-induced anaesthetic effect is adaptive, since the anaesthetic effectreduces the ability of the organism to respond effectively to ex-ternal stimuli. When animal (including human) drug users do nothave the benefit of using familiar cues to anticipate and offsetdrug effects, they experience much higher rates of overdose.5

Cue-triggered preparatory/compensatory responses tend toraise the marginal utility of consumption. For example, cue-triggered salivation and gastric secretion raise one’s appetite forfood. Numerous studies demonstrate that the presentation of foodcues elevate appetite.6 Likewise, cue-triggered hypersensitivityraises one’s valuation for an anaesthetic drug like morphine.7 Thesubjective “craving” of the decision-maker described in the story

[1980], Stewart and Eikelboom [1987], Siegel, Krank, and Hinson [1988], Turkkan[1989], and the commentaries that accompany the Turkkan paper.

2. Other domains include language, memory, social competition, aggression,play, substance abuse, pharmacology, immunology, exercise physiology, stress,digestive physiology, skeletal response systems, cardiovascular functioning, sex-ual behavior, maternal lactation, and infant suckling. See Siegel, Krank, andHinson [1988], Turkkan [1989], Hollis [1997], and Domjan, Cusato, and Villareal[2000].

3. See Mattes [1997], Rogers [1989], Simon [1986], Woods et al. [1977], andWoods [1991].

4. See Siegel [1975].5. Heroin tolerance is relatively low when heroin is injected in an environ-

ment that does not contain the set of cues associated with past use, making“overdose” from previously tolerated doses more likely in unusual injection envi-ronments [Siegel, Hinson, Krank, and McCully 1982].

6. See Booth, Lee, and McAleavey [1976], Cornell, Rodin, and Weingarten[1989], Federof, Polivy, and Herman [1997], Lambert [1991], and Weingarten[1984].

7. Clinicians commonly report that drug-associated environmental cues elicitwithdrawal symptoms and relapse in long-detoxified former addicts [Siegel,Krank, and Hinson 1988].


at the beginning of this paper provides an example of how strongthis cue-induced marginal utility effect can be. A less dramaticexample involves a smoker . . .

who had been a nicotine addict but hadn’t smoked for years. He had ab-stained from cigarettes in a variety of situations where he had smoked in thepast, and thus he had desensitized himself to a variety of conditioned asso-ciations—cigarettes at parties, cigarettes at morning coffee, cigarettes at thedesk, and so on. One day he went to the beach and was suddently over-whelmed by an intense craving to smoke. He found this beyond understand-ing until he realized that smoking on the beach had been an importantpattern at one time in his life, and that he had not had the opportunity toeliminate that particular conditioned association [Goldstein 1994, pp 221–222].8

Such cue-based motivational effects arise in a wide range ofdomains, including feeding, drug use, sexual activity, social com-petition, aggression, and exercise/play.

In summary, repeated pairings of cues and behavior elicitscue-contingent conditioned responses. Such responses are oftenfunctionally preparatory or compensatory, and effectively elevatean organism’s appetite (i.e., marginal utility) for the consumptionevent that has historically followed the anticipatory cues.

II.2. Formal Model

The following model illustrates the psychological effects dis-cussed above. It is presented as a model of drug use, but theprinciples explored below apply to many other types of habitualconsumption.

Time is discrete, indexed by the nonnegative integers, t �{0,1,2, . . . }. Each time period a random cue takes on one (andonly one) of two values: RED or GREEN.9

(1) Pr�RED� � �R

(2) Pr�GREEN� � 1 � �R � �G.

8. This quote was brought to my attention by Elster [1999].9. The analysis assumes that only two cues exist and that they are readily

distinguished. Naturally, most cues belong on a continuum. A complete model ofcues would need to evaluate consumers’ capacities to discriminate among cues(“discrimination gradient”) and consumers’ propensities to generalize from onecue to other related cues (“generalization gradient”). For example, would a heroinaddict who experiences conditioned craving when he sees his dealer also experi-ence conditioned craving when he sees his dealer’s girlfriend? For experimentalevidence on generalization gradients in nonhuman animals, see Hoffman,Fleshler, and Jensen [1963], Richardson, Williams, and Riccio [1984], and Cheng,Spetch, and Johnston [1997].


Each period the consumer chooses between two activities: anactivity that can be repeated over time, and some alternativeactivity that changes every period and hence is not capable ofbeing influenced by conditioning effects. (Recall that conditionedresponses are built up through repetitive associations betweencues and a particular consumption activity.) I will refer to therepeatable activity as the primary activity.

Each period the consumer must choose either the primary oralternative activity. This is a zero-one decision, and it is madecontingent upon the realization of the cue process. Let at

R � {0,1}represent the consumer’s action choice contingent on a RED cuein time period t. Let at

G � {0,1} represent the consumer’s actionchoice contingent on a GREEN cue in time period t. A 0 repre-sents a choice to engage in the alternative activity. A 1 representsa choice to engage in the primary activity. For example, if theconsumer were to choose at

R � 1, atG � 0, the consumer would

engage in the primary activity if the cue turned out to be REDthat period, and the consumer would engage in the alternativeactivity if the cue turned out to be GREEN.

The consumer’s physiology is characterized by two compen-satory processes: xt

R, a compensatory process activated by theRED cue; and xt

G, a compensatory process activated by theGREEN cue. When the RED cue appears, compensatory processxt

R is activated, and is strengthened or weakened according to theprocess:

(3) xt�1R � �xt

R � �1 � ��atR.

When the RED cue appears, compensatory process xtG is not

operational, and does not evolve:10

(4) xt�1G � xt

G.

The outcome is flipped when the GREEN cue appears. In thiscase, compensatory process xt

G is operational, and is strengthenedor weakened according to the process:

10. The assumption that the compensatory process does not evolve if the cueis not present is consistent with the available evidence on “extinction” (seeInstitute of Medicine [1996, pp. 42] and Hoffman, Fleshler, and Jensen [1963]).Recall the example of the ex-smoker who had not extinguished his associationbetween beach cues and smoking. Cue-based drives do not decay on their own. Thecue-conditioned addict must be desensitized by repeatedly exposing the individualto the cue while abstaining from consumption of the addictive good. Finally,assuming that the cue-based drive decays in the absence of the cue, would notchange most of the qualitative analysis.


(5) xt�1G � �xt

G � �1 � ��atG.

and compensatory process xtR is not operational and does not

evolve:

(6) xt�1R � xt

R.

These cue-sensitive transition processes imply that xtR is a

weighted average of the consumer’s past actions in periods whenthe RED cue appeared. Likewise, xt

G is a weighted average of theconsumer’s past actions when the GREEN cue appeared. Finally,note that x0

R and x0G are assumed given, and lie inside the unit

interval. This implies that all future values of xtR and xt

G also liein the unit interval.

The consumer’s instantaneous utility function is cue-contin-gent. When the RED cue appears, instantaneous utility is givenby

(7) u�atR � xt

R� � �1 � atR�,

where is the value (in utils) of the alternative activity, u� isincreasing and strictly concave, and 0 � � 1.

Likewise, when the GREEN cue appears, instantaneous util-ity is given by

(8) u�atG � xt

G� � �1 � atG�.

Four characteristics of these contingent utility functionsshould be noted.

First, the functional form of this meta-utility function is notchosen by the consumer but is instead biologically predetermined.As numerous authors have argued, conditioned responses aregenerally evolutionarily adaptive. According to Hollis [1982], “thebiological function of classically conditioned responding . . . is toenable the animal to optimize interaction with the forthcomingbiologically important event” [p. 3]. I take this dynamic system asa reliable primitive since it is supported by a large body of con-trolled experiments reported in the neuroscience, pharmacology,and psychology literatures.

Second, the instantaneous utility functions incorporate thecompensatory processes in a natural way. The compensatoryprocess offsets the effect of consumption of the primary good.Such offsetting suggests that the compensatory process in thisparticular model be interpreted as an “opponent process” [So-


lomon 1980]. Opponent processes are a particular type of com-pensatory process that partially counteracts the effect of theconsumption event.

Third, the preferences in equations (7)–(8) imply thatstrengthening of the compensatory process is hedonically aver-sive: (�u[at

i xti))/� xi � 0, i � {R,G}. This is a standard

characteristic of the compensatory processes that are associatedwith drugs of abuse. These compensatory processes are experi-enced as craving and withdrawal.11 However, aversive compen-satory processes do not apply to all habitual activities. Considerfood cues, like the smell of freshly baked bread. Food cues initiatea compensatory process characterized by appetite arousal andsalivation. In general, appetite-arousing compensatory processeselevate the level of utility experienced by the consumer if theconsumer actually does eat (i.e., consume the primary good):�u/� xi � 0, given at

i � 1. Note that this property does notcharacterize the preferences in equations (7)–(8). But, this prop-erty can be easily modeled. For example, consider preferencesgiven by u(at

ixti xt

i) � (1 ati). Adopting such preferences

would not change the results that follow.Fourth, the term in equations (7)–(8) can be motivated in

the following way: assume that the consumer gets perishableincome of $1 every period, which can be allocated to one of twoactivities—the primary activity (with price $1 per unit) or thealternative activity (with price $1) which yields utils per unit.

I assume that the consumer is infinitely lived, and the con-sumer’s instantaneous utility functions are weighted by an expo-nential discount function with discount factor �. Then the con-sumer’s value function and Bellman equation are

(9) V� xR, xG� � maxaR,aG

��R�u�aR � xR� � �1 � aR�

� �V��xR � �1 � ��aR, xG��

� �G�u�aG � xG� � �1 � aG�

� �V� xR,�xG � �1 � ��aG��.

Time subscripts have been suppressed, since all variables in theequation above are contemporaneous. This value function repre-sents the welfare of the consumer just before the current period’s

11. See Siegel, Krank, and Hinson [1988], pp. 92–93.


appearance of the cue. The first bracketed term is the consumer’swelfare conditional on the appearance of the RED cue. The secondbracketed term is the consumer’s welfare conditional on theGREEN cue. Finally, note that this Bellman equation represen-tation implies that preferences are dynamically consistent. I willrefer to equation (9) as the Cues Bellman equation.

II.3. Parallels to Becker and Murphy [1988]

The Cues Model is related to the addiction model of Beckerand Murphy. In the Becker-Murphy model, past consumption ofan “addictive” good raises the marginal utility of current con-sumption of that good.

Compensatory processes, which are embedded in the CuesModel, provide a microfoundation for the complementarity effectswhich are assumed in the model of Becker and Murphy. Recallthat the compensatory variables, xR and xG, can be interpreted as“stocks” of past consumption. The equation of motion for xi (i �{R,G}) implies that xi is a weighted average of the consumer’spast actions in periods when the cue of color i has appeared. Theinstantaneous utility function,

u�ai � xi� � �1 � ai�,

implies that a high value of xi raises the marginal utility associ-ated with consumption of the primary good (i.e., the cross-partialis positive, �2u/�ai� xi � 0, since u is concave). Drawing theseeffects together, past consumption of the primary good raises thevalue of the stock variable, which in turn raises the marginalutility of current consumption of the primary good. Hence, com-pensatory processes provide a biological microfoundation for themarginal utility effects in the Becker-Murphy model.

Because of these similarities, the Cues Model embeds theBecker-Murphy Model as a special case. Set �R � 0 or �R � 1 toretrieve a discrete choice, discrete time version of the Becker-Murphy Model. Note that setting �R to either 0 or 1 effectivelyeliminates the role of the cue. In this case, the Bellman equationcan be rewritten as

(10)

W� x� � maxa

�u�a � x� � �1 � a� � �W��x � �1 � ��a��,


where we employ a general discount factor � in anticipation ofresults which follow below. To recover a discrete choice, discretetime version of the Becker-Murphy model, set � equal to theone-period discount factor, �.

The model summarized in equation (10) captures the impor-tant qualitative properties of the Becker-Murphy Model, but thetwo models do not nest each other. First, equation (10) assumes adiscrete choice, discrete time framework in contrast to the con-tinuous-choice, continuous-time Becker-Murphy framework.More importantly, equation (10) adopts the instantaneous utilityfunction u(a x) � (1 a), where u is any concave function.Becker and Murphy use the utility function, u(a, x), where u isquadratic and concave. Despite these differences, equation (10)captures the critical qualitative properties of the Becker-Murphymodel which were discussed at the beginning of this subsection.We refer to equation (10) as the No-Cues Bellman equation.

The model summarized by the No-Cues Bellman equation isclosely related to the completely general Cues Model (equation(9)). Hence, it is helpful to begin the analysis in this paper bycharacterizing the solution of the No-Cues Bellman equation.

PROPOSITION 1. The optimal policy correspondence of the No-CuesBellman equation is a threshold rule. I.e., there existsthreshold value x such that

a � � 0 if x � x1 if x � x.

All proofs are presented in the Appendix. To develop intui-tion for this result, recall the instantaneous utility function,

u�a � x� � �1 � a�.

A high value of the compensatory process, x, raises the marginalutility associated with consumption of the primary good (i.e.,�2u/�c� x � 0). This effect is mitigated, but not completely offset,by dynamic considerations.12 When the compensatory process isstrong, consumption of the primary good is optimal, which is theresult in Proposition 1. Hence, the model is said to be character-

12. Specifically, higher current values of the compensatory process raise thefuture disutility associated with current consumption of the primary good.


ized by “adjacent complementarity”: consumption of the primarygood increases (weakly) with the stock of past consumption.13

The comparative static results for the No-Cues Bellmanequation will also prove useful for the analysis of the generalmodel.

PROPOSITION 2. The threshold value x is increasing with the dis-count factor, �, increasing with the outside option, , andincreasing with the compensatory process weighting factor,1 �.

The intuition for these effects is straightforward. First, ahigher value of the discount factor, �, implies that the futuretakes on greater weight, so current consumption of the primarygood generates more future disutility (since future values of x risewith current consumption). Hence, higher � reduces optimal con-sumption of the primary good, which implies a higher threshold xfor primary consumption. Second, a higher value of the outsideoption, , implies that the alternative good becomes relativelymore appealing, generating a higher threshold x for primaryconsumption. Third, a higher value of the weighting factor 1 �implies that current consumption of the primary good has moreimpact on values of x in the immediate future, and relatively lessimpact on values of x in the distant future. These effects net outwithout discounting, but because of discounting the near-termeffects dominate. Hence, consumption of the primary good ismore costly, which implies a higher threshold, x, for primaryconsumption.14

II.4. Solution of the Cues Bellman Equation

The Cues Model (equation (9)), is closely related to the No-Cues Model (equation (10)). Specifically, the value function in theCues Model is a weighted average of modified value functions tothe No-Cues Bellman equation.

13. The analysis in Becker and Murphy [1988] focuses on parameter valuesthat imply adjacent complementarity, but their model admits cases in whichadjacent complementarity does not arise.

14. Comparative statics with respect to cannot be signed unless morestructure is imposed on the function u. When u is linear, � x/� � 0, but thisinequality reverses when u is sufficiently bowed.


PROPOSITION 3.

V�xR,xG� ��R

1 � ��G W�xR�� R

1 � ��G��

�G

1 � ��R W�xG�� G

1 � ��R�.

Recall that W( � �� y) represents a solution to the No-CuesBellman equation assuming a discount factor of � � y. In essence,Proposition 3 implies that the Cues Model is a superimposition oftwo versions of the No-Cues Model. The first term, �R/(1 ��G)W( xR�� R/(1 ��G)), represents the discounted valueof payoffs that occur when the RED cue is present. The secondterm, �G/(1 ��R)W( xG�� G/(1 ��R)), represents thediscounted value of payoffs that occur when the GREEN cue ispresent. This additive separability arises because the RED andGREEN compensatory processes temporarily “hibernate” whenthe other cue appears. For example, when the GREEN cue ispresent, the RED process does not influence instantaneous utilityand does not evolve.

However, the Cues Model is not an exact superimposition oftwo No-Cues Models, since the modified discount factors, ��R/(1 ��G) and ��G/(1 ��R), are both less than � (the truediscount factor). These modified discount factors reflect the prop-erty of the Cues Model that current consumption of the primarygood only has an impact on future periods in which the cuerealization is the same as the current cue realization. This effectmitigates the future cost of current primary good consumption,and is captured by adopting a lower discount factor in the calcu-lation of W. Heuristically, ��R/(1 ��G) is just the expectedvalue of the discount factor that will apply between the currentperiod and the next period in which the RED cue is present:

�R� � �G�R��2 � ��G�2�R��3 � . . . � ��R/�1 � ��G�.

Likewise, ��G/(1 ��R) is just the expected value of the discountfactor that will apply between the current period and the nextperiod in which the GREEN cue is present.

Finally, the terms that weight the value functions in Propo-sition 3 adjust the future weightings so that the sum of weightsover all future RED periods and all future GREEN periods are,respectively, equal to �R/(1 �) and �G/(1 �). For example,


�R

1 � ��G �1 � � ��R

1 � ��G� � � ��R

1 � ��G�2

� . . . � ��R

1 � �.

A formal proof of Proposition 3 appears in the Appendix.Using Proposition 3 and our earlier results on threshold rules

and comparative statics in the No-Cues Model (Propositions 1and 2), we are now in a position to characterize the optimal policyassociated with the Cues Model.

COROLLARY 4. The optimal policy correspondence of the Cues Bell-man equation is a threshold rule. I.e., there exist thresholdvalues xR and xG such that

aR � � 0 if xR � xR

1 if xR � xR

aG � � 0 if xG � xG

1 if xG � xG.

Without loss of generality assume that �R � �G. Then xR �xG � x, where x is the threshold value from the optimalpolicy generated by the No-Cues Bellman equation (� � �).

This threshold rule follows from Propositions 1 and 3: athreshold rule solves the No-Cues Model, and the Cues Model isa superimposition of two modified versions of the No-Cues Model,so the Cues Model also generates a threshold rule.

The inequality, xR � xG � x, follows from Proposition 2. Thecomparative statics results in Proposition 2 imply that the opti-mal threshold value falls with the discount factor. When �R � �G,the effective discount factors in Proposition 3 obey the inequali-ties, ��R/(1 ��G) � ��G/(1 ��R) � �, implying that xR �xG � x. Intuitively, relative to the No-Cues Model, the CuesModel implies that today’s consumption is less likely to affecttomorrow’s utility flow since tomorrow the consumer may expe-rience the other cue. This makes consumption of the primary goodmore appealing, lowering the threshold values below x.

Proposition 2 also generalizes to the Cues Model.

COROLLARY 5. The threshold value xR is increasing with the dis-count factor �, increasing with the outside option , increas-ing with the compensatory process weighting factor 1 �,and increasing with the probability of the RED cue, �R. Thethreshold value xG changes with the same signs, except xG


increases with the probability of the GREEN cue, �G � 1 �R.

These results follow from the fact that the Cues Model is asuperimposition of two No-Cues Models, in which the discountfactor, �, is replaced by the effective discount factors, ��R/(1 ��G) and ��G/(1 ��R). Note that these effective discountfactors both increase with �, while the first discount factor in-creases with �R, and the second discount factor increases with�G. Higher (effective) discount factors imply higher thresholds forconsumption of the primary good, since the future is effectivelyweighted more heavily.

III. INTERPRETATION AND ANALYSIS

III.1. Dynamics and Steady States

The model described above has two state variables: xR andxG. The evolution of the state variables is characterized by fourbasins of attraction in �xR, xG� space (Figure I).

For example, consider an actor with physiological state vari-

FIGURE ISteady States and Basins of Attraction


http://www.mitpressjournals.org/action/showImage?doi=10.1162/003355301556356&iName=master.img-000.png&w=299&h=191

ables �xtR, xt

G� lying in the interior of the North-West basin ofattraction in Figure I. This implies that

0 � xtR � xR

xG � xtG � 1,

where xR and xG are the threshold values from Corollary 4. Theseinequalities imply that the RED cue elicits a relatively weakconditioned compensatory response ( xt

R) and the GREEN cueelicits a relatively strong conditioned compensatory response( xt

G). By Proposition 1, atR � 0, and at

G � 1: the consumer choosesthe alternative activity when the cue is RED, and chooses theprimary activity when the cue is GREEN.

These cue-contingent actions can be used to derive the one-period evolution of the state variables. If the cue realized inperiod t is RED, then

xt�1R � �xt

R � �1 � ��atR � �xt

R � xtR

xt�1G � xt

G.

If the cue realized in period t is GREEN, then

xt�1R � xt

R

xt�1G � �xt

G � �1 � ��atG � �xt

G � �1 � �� xtG.

Hence, either xtR will fall, or xt

G will rise, and hence �xt�1R , xt�1

G � willlie in the North-West basin of attraction. Given the iid distribu-tion of the cue realization, the two state variables will convergewith probability one to a steady state �xR, xG� � �0,1�.15 A simu-lated partial convergence path is drawn in Figure I.

In the preceding analysis, the weak conditioned compensa-tory response elicited by the RED cue is self-reinforcing. Theweak compensatory response implies that it is optimal for theconsumer to choose the alternative activity in the presence of theRED cue. This further weakens the compensatory process asso-ciated with the RED cue. Likewise, the strong conditioned com-pensatory response elicited by the GREEN cue is self-reinforcing.This strong compensatory response implies that it is optimal for

15. A steady state exists at time period T if the state variables are constantfrom T forward:

�x tR � �xt

W � 0 � t � T.


the consumer to choose the primary activity in the presence of theGREEN cue. This further strengthens the compensatory processassociated with the GREEN cue.

The discussion above has focused on one of the four basins ofattraction. Analogous arguments apply to the other basins ofattraction.

COROLLARY 6. Fix parameters for the Cues Model. Assume thatthese parameters generate threshold values xR and xG in theinterior of the unit interval. Then, there exist four locallystable steady states:

�xR, xG� � �0,0��0,1��1,0��1,1�.

The existence of these four steady states follows from argu-ments analogous to those described at the beginning of this sub-section. These arguments depend on both Proposition 1 and theequations of motion for the state variables, equations (3)–(6).

The two steady states in the Cues Model that are character-ized by no cue-sensitivity (�xR, xG� � �0,0� and �xR, xG� � �1,1�)are analogs of the “no addiction” and “addiction” steady states ofBecker and Murphy [1988]. In the �0,0� steady state of the CuesModel, the optimal action is to never engage in the primaryactivity, regardless of the cue outcome. In the �1,1� steady state ofthe Cues Model, the optimal action is to always engage in theprimary activity, regardless of the cue outcome.

III.2. Cue-Sensitivity

The difference between the Cues Model and the Becker-Murphy Model is highlighted by the two steady states in whichbehavior is cue-sensitive: �xR, xG� � �0,1� and �xR, xG� � �1,0�. Inthese steady states, the actions of the consumer depend on real-izations of the cue process. For example, at the �0,1� steady state,the consumer engages in the alternative activity when the cue isRED and engages in the primary activity when the cue isGREEN. Hence, actions depend on the cue process, even thoughthe cue process is arbitrary in the sense that the sequence of cuesis independent of all other exogenous variables in the consumer’sproblem. Conditioned responses explain how “neutral” cues cometo generate “real” effects. The intuition behind this result is


straightforward. A cue matters because the cue has been associ-ated previously with primary consumption; this association hasgenerated a cue-contingent compensatory process, which createsa cue-contingent marginal utility effect, which leads the con-sumer to choose actions that reinforce the association betweencues and primary consumption.

III.3. Cue-Management

If cues affect welfare, then one would expect that consumerswill attempt to influence those cues. One way to calibrate theimportance of cue effects is to ask how much a consumer wouldpay to control the cue process. It is helpful to recall the earliermotivation for the term in the instantaneous utility function:“Assume that the consumer gets perishable income of $1 everyperiod, which can be allocated to one of two activities: the primaryactivity (with price of $1 per unit) or the alternative activity (withprice $1) which yields utils per unit.” I want to measure theconsumer’s willingness to give up this income, in return for thecapacity to permanently control the cue process. The next Prop-osition shows that the willingness to pay can be made arbitrarilyclose to all of the consumer’s income.

PROPOSITION 7. For any � � 1, there exist preferences and cueprobabilities that support a steady state at which the con-sumer is willing to give up at least � proportion of herpermanent income to permanently control the cue process.No such parameterization exists if � � 1.16

This proposition is proved in the Appendix. The idea behindProposition 7 is that a parameterization can be found whichdrives the consumer’s payoff at a particular steady state to u(0)/(1 �). For intuition, consider the case where is close to one(making the compensatory process very effective), �R is close toone (making the RED cue very common), xR is one (making theRED compensatory process strong), and xG is zero (making theGREEN compensatory process weak). Then, subject to two othernecessary conditions, the consumer is at a steady state in whicha realization of the RED cue induces a strong compensatoryresponse that makes consumption of the primary good optimal.

16. For scenarios in which the consumer gives up � � 1 proportion of income,I assume zero consumption of the primary good and negative consumption of thealternative good. E.g., if income is 1 � � 0, then consumption of the alternativegood is 1 � units generating (1 �) utils.


This consumer would give up almost all of her permanent incometo force the cue to be GREEN for all future t.

Proposition 7 formalizes the prediction that cues play a po-tentially important role in welfare analysis.17 These predictionsmatch up well with reality. Cue-management is a commonlyobserved behavioral and therapeutic technique. Real-life consum-ers routinely manipulate the cues that they experience. For ex-ample, ex-alcoholics avoid bars, dieters keep snack food out ofview, and parents choose the candy-free checkout aisles at super-markets.18 One weight management program offers the followinganalysis:

Jar of candy on the desk . . . sure I’ll have some. Strolling past a bak-ery . . . the donuts sure smell good. Popcorn at the movies . . . I can’t resist.Snacks while watching TV . . . the whole family does it. It’s just about im-possible to isolate yourself from food and the various signals that remind youof food. In our society, we’re bombarded with tempting treats that lure us intounplanned eating episodes. So what can you do? [. . .] You can eliminate sometriggers, such as bowls of candy sitting on your desk. You can stop buyingfoods where “you can’t eat just one” [Wellbridge Weight Management Ap-proach 1998, Section 5, p. 8].

In addition, “cue-desensitization” techniques are now beingused by therapists with patient populations suffering from pho-bias and addictions [Jansen 1998; Monti et al. 1993; Wardle1990]. For example, one recently developed technology

places the addict seeking treatment in an immersive virtual reality rig.While a headset displays a video from a laser disc, sensors monitor respira-tion rate, pulse rate, perspiration and skin temperature; therapists correlatespikes in bodily responses to particular scenes from the videodisc. Once thetriggers are identified, [the company] exposes its clients to the most provoca-tive scenes over and over again. By watching the instrumentation readouts,the subjects learn to suppress their cravings [Brody 1999, p. 29].

In terms of the Cues Model, cue-desensitization techniques helpaddicts lower the value of the cue-contingent compensatory pro-cesses, xR and xG.19

17. At the Becker-Murphy steady states the consumer is unwilling to give upany income to control the cue process. At these steady states cues affect neitheractions nor welfare.

18. Alternatively, these decisions can be explained with dynamically incon-sistent preferences.

19. Analogously, Becker-Murphy consumers who experience aversive addic-tions would like to be able to lower their accumulated consumption capital.


III.4. A Different Cue Structure

So far, I have assumed that the cue process is independent ofthe other exogenous variables in the consumer’s problem. Thisassumption leads the model to understate the importance andlikelihood of cue-sensitivities. I now discard this assumption.This modeling switch is sensible, since most real-world cues arehighly correlated with reward opportunities. For example, it isdifficult to smoke a cigarette without first seeing one—i.e., seeinga cigarette cue:

Contrary to what most people might think, craving is not provoked by theabsence of the drug to which a person was addicted, but by its presence—thatis, by its availability. This is illustrated by the nicotine addict who goesskiing for a whole day, leaving cigarettes behind. No thought is given tocigarettes—they are simply unavailable. Then back at the lodge, wherenicotine is available again, intense craving strikes, and the addict lights up[Goldstein 1994, p. 222].20

With the experience of the skier in mind, consider the follow-ing slightly altered version of the earlier model. The new modeland the old model are identical except that in the new model, theconsumer can only engage in the primary activity when the cue isRED. This is a physical constraint on the consumer. For example,imagine that a consumer can only smoke a cigarette (i.e., engagein the primary activity) when she experiences the cigarette avail-ability cue (i.e., sees the RED cue).

With these assumptions, the consumer’s value functionbecomes

(11) V� xR,0� � maxaR,aG

��R�u�aR � xR� � �1 � aR�

� �V��xR � �1 � ��aR,0�� . . .

� �G�u�0� � � �V� xR,0��.

Note that this value function is derived by simply setting xG, aG �0 in the old value function; aG � 0 since the GREEN cue signalsthe lack of feasibility of engaging in the primary activity; xG � 0since xG is a weighted average of the consumer’s past choices ofaG.21 I refer to this as the Restricted Cues Model.

20. This passage was brought to my attention by Elster [1999].21. I have also set x0

G � 0. This is equivalent to the assumption that theconsumer has lived long enough for the GREEN compensatory process to havedecayed effectively to zero.


Recall that the value function represents the welfare of theconsumer before the current period’s realization of this cue. Thefirst bracketed term in equation (11) is the consumer’s welfare,conditional on the appearance of the RED cue (i.e., conditional onthe primary activity being available for consumption). The secondbracketed term is the consumer’s welfare, conditional on theappearance of the GREEN cue (i.e., conditional on the primaryactivity being unavailable for consumption).

The characterization of the general Cues Model (Proposition3) can be applied to this special case.

COROLLARY 8.

V�xR,0� ��R

1 � ��G W�xR�� R

1 � ��G� ��G

1 � ��u�0� � �.

The first term, �R/(1 ��G)W( xR�� R/(1 ��G)),represents the discounted value of payoffs that occur when theRED cue is present. The second term, �G/(1 �)(u(0) � ),represents the discounted value of payoffs that occur when theGREEN cue is present. During periods in which the GREEN cueis present, the instantaneous payoff must be u(0) � . Hence, inProposition 3 the term W( xG�� G/(1 ��R)) is replaced by

u�0� �

1 � ��G/�1 � ��R� ,

which yields Corollary 8.The value function in Corollary 8 is just a positive linear

transformation of the value function associated with the No-CuesModel (given � � ��R/(1 ��G)). Hence, the value function inCorollary 8 is associated with a maximization problem in whichthe instantaneous utility function is a positive linear transforma-tion of the instantaneous utility function in the No-Cues Model.Note that optimal policy correspondences do not change when aninstantaneous utility function is translated in this way. Hence,Proposition 1 and Corollary 8 jointly imply that the optimal policycorrespondence of the Restricted Cues Model is a threshold rule.

COROLLARY 9. The optimal policy correspondence of the RestrictedCues Bellman equation is a threshold rule. I.e., there exists athreshold value xR such that

aR � � 0 if xR � xR

1 if xR � xR.


In addition, xR � x, where x is the threshold value from theoptimal policy generated by the No-Cues Bellman equationwith � � �.

III.5. Commitment as Cue-Management

Subsection III.3 showed that consumers are willing to give upresources to eliminate certain cues. In the Restricted Cues Model(introduced in the previous subsection), such cue-elimination isequivalent to a voluntary reduction in the consumer’s choice set.In the Restricted Cues Model cues are inextricably linked tochoice sets. (If “smoke a cigarette” is in my choice set, then Ipossess a cigarette or am able to acquire one, either of which is asmoking cue.)

I adopt the term “pseudo-commitment” to describe a person’sdecision to reduce her own choice set for the purposes of cue-management. Contrast pseudo-commitment with “classical” com-mitment, which is driven by dynamically inconsistent prefer-ences. Pseudo-commitment is like classical commitment, becausepseudo-commitment implies that consumers will take potentiallycostly actions which reduce their future choice sets (like inten-tionally not bringing cigarettes on an outing). But pseudo-com-mitment differs from classical commitment, because the motivefor pseudo-commitment is cue-management. Note that consum-ers modeled in the current paper have dynamically consistentpreferences. Pseudo-commitment is driven by the property thatcue exposure is hedonically aversive.

In the Restricted Cues Model, the consumer is willing to giveup potentially all of her income to achieve cue-management.Since cues and choice sets are linked, this willingness impliesthat the consumer will potentially engage in highly costlypseudo-commitment.

COROLLARY 10. For any � � 1, there exist preferences and cueprobabilities of the Restricted Cues Model that support asteady state at which the consumer is willing to give up atleast � proportion of her permanent income to permanentlydeny herself access to the primary activity. No such param-eterization exists if � � 1.

The intuition behind the corollary parallels that of Proposi-tion 7.


III.6. Impulsivity as Cue-based Drive

Cue-based models predict that actors will exhibit high levelsof short-run impatience when exposed to reward-availabilitycues.22 Intuitively, cues initiate physiological changes that primeorganisms for immediate consumption. When this has occurred,delaying consumption is costly. The consumer must be generouslycompensated to induce her to willingly resist immediate gratifi-cation of a cue-based drive. The following analysis formalizes thisintuition.

Recall the Restricted Cues Model, and consider a consumerwho is in steady state �xR, xG� � �1,0�. Consider the followingprocedure, which experimentally evaluates the consumer’s pa-tience. At time 0, show the consumer the primary consumptiongood, which, for discussion, is assumed to be a cigarette. Tell theconsumer she can either smoke one cigarette at period � or 1 � ��

cigarettes at � � 1. This procedure exposes the consumer to thecigarette cue at period 0 and in the period chosen for consump-tion.23 Finally, assume that no other consumption occurs duringthe course of this experiment. In summary, the subject is offeredthe following two consumption streams:

. . . t � � t � � � 1 . . .

Stream A: 0 1 0 0Stream B: 0 0 1�� 0.

Assume that the subject picks �� to induce indifference be-tween Streams A and B. To simplify analysis, assume that theperiods are sufficiently short so that it is appropriate to set � �� 1.

If � � 0, then �0 is the solution to the equation,

(12) u�1 � xR� � u�0� � u� xR� � u�1 � �0 � xR�,

where xR � 1, (recall the steady state assumption). The left-handside of equation (12) represents the instantaneous payoff ofStream A during periods t � � � 0 and t � � � 1 � 1. Thecue-induced compensatory process appears in the first term butnot the second term on the left-hand side. The cigarette cue is

22. The ideas in this subsection developed from a conversation with JeroenSwinkels.

23. Alternatively, one could assume that the cigarette will be present untilthe decision-maker smokes it. This would not change the qualitative results. Anearlier version of the paper analyzes this case.


present in period 0 for two reasons: the choice question is posed inperiod 0, and the good is consumed in period 0.

The right-hand side of equation (12) represents the payoff ofStream B during periods t � 0 and t � 1. The compensatoryprocess appears in both terms on the right-hand side since the cueis present in period t � 0, the period in which the choice questionis posed, and in period t � 1, the period in which consumptiontakes place.

If u� is linear, then �0 � . The extra �0 � cigarettescompensate the respondent for failing to satisfy the cue-basedcraving in period 0. This craving is strengthened when u� isstrictly concave, and in this case �0 � .

If � � 1, then �� is the solution to the equation,

(13) u�1 � xR� � u�0� � u�0� � u�1 � �� xR�.

The left-hand side of equation (13) represents the payoff ofStream A during periods t � � and t � � � 1 (given � � 1). Thecompensatory process appears in the first term on the left-handside, but not in the second term. The cue is present in period �since Stream A implies that the good is consumed in period �.Similarly, the right-hand side represents the payoff of Stream B.The compensatory process appears in the second term on theright-hand side since Stream B implies that the good is consumedin period � � 1.

Regardless of the curvature of u�, equation (13) implies that��1 � 0. Intuitively, the respondent does not need to be com-pensated for the delay between periods � and � � 1 since con-sumption in period � is just as rewarding as consumption inperiod � � 1, as long as � � 1. Only period � � 0 is special, sincethe respondent experiences a cue-induced craving in period 0whether or not consumption of the primary good takes place.Posing the cigarette choice question in period 0 exposes the sub-ject to a cigarette cue and elevates the marginal utility ofconsumption.

Now consider an almost identical experiment, which differsonly because the alternative good is now used. The subjectchooses between one unit of the alternative good in period �, or1 � �� units at � � 1. Again, �� is chosen to yield indifferencebetween the two streams. For all � � 0, �� solves the equation: �(1 � ��). The left-hand side of this equation represents the payoffof Stream A during period t � � and the right-hand side of the


equation represents the payoff of Stream B during period t � � �1. Hence, �� 0.

How would a naive experimenter use these data to imputediscount factors? A standard approach would use magnitudes like�0, ��1, and �� as estimates for discount rates. What would thisimply? Recall that ln(�) is the actual discount factor of theconsumer in this problem. Combining results yields

�0 � � ��1 � �� 0 � ln��.

Hence, the Cues Model predicts that the experimenter willinfer falling discount rates if the experiment is conducted with a“primary” good, and a constant zero discount rate if the experi-ment is conducted with an “alternative” good. The intuition forthe former result rests with the cravings that result from theactivation of the compensatory process. When a subject first seesa consumption cue for a primary good, she experiences a compen-satory process and prefers to consume the good contemporane-ously with the compensatory process (i.e., in period 0). If shecannot consume the good in period 0, then she has relatively littlepreference for one future period versus any other. In summary,the Cues Model draws a distinction between period 0—when thecue-induced craving has been activated by the choice exercise—and all future periods—when the cue-induced craving will bepresent only if consumption actually occurs. Seeing, and thinkingabout the primary good in period 0, creates a craving for imme-diate consumption in period 0.

These predictions match experiments summarized inMischel, Shoda, and Rodriguez [1992]. The experiments identifycognitive manipulations that enable children to delay gratifica-tion. The experimenters gave their subjects the opportunity toeither consume a small reward immediately (say, one marshmal-low) or wait for a larger reward (say three cookies). During theexperiment, both rewards were within reach of the subject. At thebeginning of the session, the experimenter told the subject thatthe experimenter would temporarily leave the room, and that thesubject would be allowed to consume the larger reward when theexperimenter returned. The subject was also told that she couldring a bell, thereby ending the experiment and enabling thesubject to immediately consume the smaller reward, forgoing thelarger one. Waiting time was used as a measure of patience.

In one condition, both rewards were covered when the experi-


menter left the room. With covered rewards, preschool childrenwaited an average of eleven minutes. By contrast, uncoveringeither or both of the rewards reduced average waiting time tounder six minutes. Hence, Mischel et al. find that reward expo-sure reduces willingness to wait for a delayed reward, even whenthe reward being exposed is the delayed reward.

Laboratory and field studies of time preference find thatdiscount rates are much greater in the short run than in the longrun. Hyperbolic discount functions capture this property (e.g., seeAinslie [1992]). The analysis of this subsection, and the experi-ments reported in Mischel, Shoda, and Rodriguez [1992] suggestthat at least some of the hyperbolic discounting effects reflectcue-based drives for immediate consumption.

IV. A NEW VIEW OF HABITUATED CONSUMPTION

The predictions of the Cues Model contrast with the predic-tions of Becker and Murphy’s [1988] habit formation model inthree ways.

First, the Cues Model provides a new framework for under-standing high frequency variation in craving/marginal utility.Becker and Murphy [1988] argue that consumption binges aredriven by variation in different kinds of consumption capital.Becker and Murphy call these “weight” and “eating” capital, andassume that the former is a substitute and the latter a comple-ment to eating:

Assume that a person with low weight and eating capital becameaddicted to eating. As eating rose over time, eating capital would rise morerapidly than weight because it [is assumed to have] the higher depreciationrate. Ultimately, eating would level off and begin to fall because weightcontinues to increase. Lower food consumption then depreciates the stock ofeating capital relative to weight, and the reduced level of eating capital keepseating down even after weight begins to fall. Eating picks up again only whenweight reaches a sufficiently low level. The increase in eating then raiseseating capital, and the cycle begins again [Becker and Murphy 1988, p. 694].

The Becker-Murphy model predicts that consumption bingesare cyclical. However, the available clinical evidence suggeststhat craving episodes and the binges they induce repeatedly arisewith little or no warning and even occur for addicts who havebeen detoxified for months. Recall the heroin user who experi-enced a craving in his old neighborhood and the smoker whoexperienced a craving on the beach. Cravings often arise unpre-


dictably and are “elicited by cues that were associated with drugavailability and drug use in the ex-addict’s previous experience”[Goldstein 1994, pp. 220–221]. In addition, if an addict experi-ences a small taste, or “priming” dose of the addictive substance,he will experience extremely strong cravings [Gardner and Low-inson 1993]. Such tastes are themselves an important consump-tion cue.24 The Cues Model predicts that seemingly trivial varia-tion in situational cues can elicit temporary but powerful changesin marginal utility. These effects arise in the consumption of awide range of goods. “Impulse buying” and unplanned consump-tion are subjects of active study by retail firms and marketingexperts. For example, surveys find that between 20 percent and50 percent of supermarket purchases are unplanned, and thatmost of these unplanned sales are catalyzed by in-store stimuli.25

The Cues Model explains much of this behavior, predicting whichfamiliar stimuli—e.g., drug cues, food cues, sexual stimuli,26 so-cial stimuli27—will cause preferences to vary from moment tomoment.28

Second, the Cues Model explains why and how consumerswork to overcome/regulate their habituated appetites. In theBecker and Murphy model, staying in the addicted state is anoptimal policy. Addicted consumers would like, in principle, tohave less consumption capital, but there is no way for them tooptimally achieve this. In the Cues Model, addictive/habitualconsumption will be resisted by addicts who can control theirenvironmental cues. The Cues Model predicts many of the specificcue-management and quasi-commitment strategies that habitualconsumers commonly use to regulate their own appetites (e.g.,hide cigarettes, avoid parties where alcohol will be served, use thecandy-free checkout lane, “store tempting treats in ‘see proof’containers,”29 etc.). The model also predicts the successful strat-egies that people use to delay gratification (e.g., distract oneself

24. See also Institute of Medicine [1996, p. 46].25. See Abratt and Goodey [1990].26. See Domjan, Cusato, and Villareal [1999] and Loewenstein, Nagin, and

Paternoster [1997].27. See Domjan, Cusato, and Villareal [1999].28. See McSweeny and Bierley [1984] for additional work on the relationship

between conditioned responses and consumer behavior. In addition, several au-thors have argued that exposure to credit card insignia elicits conditioned re-sponses. Some existing experiments support this implication. See Feinberg [1986]and McCall and Belmont [1996]. In addition, Prelec and Simester [1998] find thatallowing subjects to pay with credit cards raises mean auction bids for goods ofuncertain value by approximately 75 percent.

29. E.g., see Wellbridge Weight Management Approach [1998].


during the waiting period).30 Moreover, the Cues Model predictsmany of the strategies that firms use to encourage consumers tomake purchases (e.g., install hotel minibars in which snacks andalcohol are visible even if the minibar has not been opened,generate artificial appetite-arousing food smells in supermarkets,package snack food in see-through containers, visually displaydessert options in restaurants, “place candy and gum in all[checkout] lanes to take advantage of impulse buying,”31 etc.). TheCues Model explains how firms create temptation and how/whyconsumers sometimes avoid it.

Third, the Cues Model explains many of the public dimen-sions of habitual consumption. The Cues Model implies that cuescan be a negative externality. When an individual experiences afood cue (e.g., smell of freshly baked cookies), he will feel an urgeto eat. If he is unable to eat, the exposure to the cue will have beenaversive. Think how aversive it would be to watch someone elseeat a meal if you were not able to join in. The Cues Model impliesthat food consumption is a jointly complementary activity. Eatingshould be done as a group. Hence, norms develop to discourageindividuals from eating in a public space if others are not alsoable to eat (e.g., on an airplane, or in a meeting, or at a meal ifone’s companion’s food has not arrived). Firms respond to thesenorms by carefully timing the presentation of cues (e.g., goodwaiters try to bring all the entrees to the table simultaneously). Ifone does need to eat in front of somebody else, the common normis to offer to share one’s food, or to wait until the other person’sfood arrives. These externalities are particularly strong in thecase of drug use. The Cues Model predicts that some addicts andall ex-addicts will be strong supporters of laws that restrict publicsmoking and public drinking: “With nicotine, someone else’ssmoking is a potent conditioned cue for lighting up; and that iswhy regulations that establish smoke-free environments are sohelpful to nicotine addicts and ex-addicts in reducing their con-sumption or maintaining their abstinence” [Goldstein 1994, p.222]. The negative externalities of public cues may also extend tocues that appear in advertisements. In the United States, adver-tising for gambling, cigarettes, and alcohol is heavily regulated,

30. See Mischel, Shoda, and Rodriguez [1992] and Jansen [1998].31. See Wellman [1999].


and has at times been completely banned.32 Such restrictions arenot predicted by the Becker-Murphy model.

The Cues Model bears much in common with Loewenstein’s[1996] analysis of visceral factors, “which include drive statessuch as hunger, thirst and sexual desire, moods and emotions,physical pain, and craving for a drug one is addicted to. Thedefining characteristics of visceral factors are, first, a direct he-donic impact (which is usually negative), and second, an effect onthe relative desirability of different goods and actions” [p. 272]. Inthe Cues Model, some cues may endogenously become associatedwith consumption of an addictive good, and when this happensexposure to the cue can be aversive (holding actual consumptionconstant).33 Moreover, exposure to the cue will temporarily ele-vate desire for and consumption of the addictive good. In thissense, the Cues Model is a special case of Loewenstein’s moregeneral framework. Both the Cues Model and Loewenstein’sanalysis describe a world in which behavior changes rapidly frommoment to moment, temptations can/should be actively avoided,and public consumption can be a negative externality.

The Cues Model also has much in common with Romer’s[2000] model of the physiological microfoundations of preferences.Both the Cues Model and Romer’s model use conditioned learningas a microfoundation for preference formation. Although it wasdeveloped independently, the Cues Model provides an example ofa particular formalization of both Loewenstein’s and Romer’sanalysis.

V. CONCLUSION

Conditioned responses explain why cues influence motiva-tional states and behavior. Models that incorporate conditionedresponses explain a wide range of ostensibly puzzling behavior,including endogenous cue sensitivities, costly cue-management,commitment, and high levels of measured short-term impatience.The Cues Model provides a new framework for understandingaddictions. In the Cues Model behavior changes rapidly from

32. For example, since 1934, Federal law and FCC regulations have prohib-ited broadcasts of gambling advertising. Recently these restrictions have beenlegally challenged with mixed success. See United States District Court, D. NewJersey [1997] and United States Court of Appeals, Fifth Circuit [1998].

33. The aversiveness of cue-exposure depends on the form of preferences. Ifpreferences take the form u(at

ixti xt

i) � (1 ati), then activation of a

cue-conditioned compensatory process may be desirable.


moment to moment, temptations should sometimes be activelyavoided, and public consumption can generate a negative exter-nality. This paper illustrates the broader phenomenon that phys-iology influences preferences. Conditioned cues provide one im-portant physiological lever. Understanding the relationshipbetween physiological mechanisms and preferences will advancemodels of behavior.

APPENDIX: PROOFS

Proof of Proposition 1. The proof is divided into four lemmas.

LEMMA 11. Let

f�x� � t�0

�

�t�u� �tx� � �

g�x� � t�0

�

�t�u�1 � ��tx � 1 � �t��.

Then, if these functions cross, there exists a unique intersec-tion point, and f� crosses g� from above.

Note that f� is the payoff function from consuming thealternative good in all current and future periods, and g� is thepayoff function from consuming the primary good in all currentand future periods.

Proof of Lemma 11. By concavity of u,

f�� x� � t�0

�

�t� �t�u�� tx�

� t�0

�

�t� �t�u��1 � ��tx � 1 � �t��

� g�� x�. �

LEMMA 12. Let

f �x� � u�1 � x� � t�1

�

�t�u� ��tx � �t 1�1 � ��


g�x� � u� x� � � t�1

�

�t�u�1 � ��tx � 1 � �t 1��.

Then,

f � x� � f� x� f g� x� � f � x�

g� x� � g� x� f f� x� � g� x�.

Note that f � is the payoff function from consuming theprimary good in the current period and the alternative good in allfuture periods. Similarly, g� is the payoff function from consum-ing the alternative good in the current period and the primarygood in all future periods.

Proof of Lemma 12. We will show that f ( x) � f( x) f g( x) �f ( x), and omit the parallel argument that shows that g( x) �g( x) f f( x) � g( x). Let

�0� x� � u�1 � x� � u� x� �

�i� x� � u� ��ix � �i 1�1 � �� u� �ix� �i � 1�

�i� x� � u�1 � ��ix � 1 � �i��

u� ��ix � �i 1�1 � �� i � 1�,

where x represents xt. Note that �i represents the differencebetween the (t � i)th period instantaneous utility flow generatedby f ( x) and the (t � i)th period instantaneous utility flow gen-erated by f( x). Likewise, �i represents the difference between the(t � i)th period instantaneous utility flow generated by g( x) andthe (t � i)th period instantaneous utility flow generated by f ( x).Note that

g� x� � f � x� � i�1

�

�i�i� x�

� i�1

�

�i��i� x� � j�0

i 1

�j� x� � k�0

�

�k�k� x��since ¥i�1

� �i( ¥j�0i 1 �j( x) � ¥k�0

� �k�k( x)) � 0. Assume thatf ( x) � f( x). Then, ¥k�0

� �k�k( x) � 0. Hence, to show that g( x) �f ( x), it is sufficient to show that �i( x) ¥j�0

i 1 �j( x) � 0 for all i �


1. This last inequality follows from concavity of u and the factthat �x � (1 �) � x for all x in the unit interval. �

LEMMA 13.

f�x� � g�x�f f�x� �f �x�

g�x� � f�x�f g�x� � g�x�.

Proof of Lemma 13. Suppose that f( x) � g( x) and f( x) �f ( x). Then f ( x) � g( x), which implies that f( x) � f ( x), byLemma 12. This contradiction proves the required result. A simi-lar argument proves the second half of this lemma. �

LEMMA 14. The solution to the No-Cues Bellman equation

(14) W�x� � maxa

�u�a � x� � �1 � a� � �W��x � �1 � ��a��

is given by

W�x� � � f �x� if x � xg�x� if x � x,

where x is the unique crossing point of f� and g�. If f(x) � g(x)for all x, then x � �. If f(x) � g(x) for all x, then x � �.

Proof of Lemma 14. Confirm that the Bellman equation issatisfied for the candidate function W�. Specifically, divide thestate space into four regions. First, consider the region charac-terized by the inequalities: x � x and �x � (1 �) � x. In thisregion f( x) � g( x) by Lemma 11, and

W� x� � f� x� by assumption

� max � f� x�, f� x�� by Lemma 13

� maxa

�u�a � x� � �1 � a� � �f��x � �1 � ��a��

by definition of f and f� max

a�u�a � x� � �1 � a� � �W��x � �1 � ��a��

by definition of W.

Now, consider the region characterized by the inequalities: x � xand �x � (1 �) � x. In this region f( x) � g( x), by Lemma 11,and


W� x� � f� x� by assumption

� max � f� x�, g� x�� by Lemma 13

� maxa

�u�a � x� � �1 � a�� f��x�� a�g��x � 1 � ��

by definition of f and g� max

a�u�a � x� � �1 � a� � �W��x � �1 � ��a��

by definition of W.

Parallel arguments apply for the cases in which x � x, confirmingthat the Bellman equation is satisfied for the candidate functionW�. �

Lemma 14 implies that the optimal policy generates payofffunction f( x) when x � x, and the optimal policy generates payofffunction g( x) when x � x. Payoff f( x) implies permanent absti-nence from the primary good. Payoff g( x) implies permanentconsumption of the primary good. Hence, the optimal policy is athreshold rule, completing the proof of Proposition 1. �

Proof of Proposition 2. By Lemma 14, the threshold value x isthe unique crossing point of the functions f( x) and g( x), definedin the statement of Lemma 11. Let � represent a parameter ofinterest in the model. Then by the implicit function theorem,

dxd�

�f�� x,� � � g�� x,� �

gx� x,� � � fx� x, � �.

Note that gx( x,� ) fx( x,� ) � 0, by Lemma 11. So dx/d� takesthe same sign as f�( x,� ) g�( x,� ).

To calculate the comparative static on the discount factor, �,note that

f�� x, �� i�1

�

i�i 1u� �ix��

�1 � ��2 � i�0

�

�if��i�1x�

g�� x, �� i�1

�

i�i 1u�1 � ��ix � 1 � �i��

� i�0

�

�ig��i�1x � 1 � �i�1�.

Note that f(�i�1x) � g(�i�1x � 1 �i�1) @i, since f and g are


decreasing functions, �i�1x � x � �i�1x � 1 �i�1 @i, andf( x) � g( x). So f�( x,�) g�( x,�) � 0.

The comparative static on is trivial, since f( x,) g( x,) � 1/(1 �) 0 � 0.

To calculate the comparative static on �, note that

f�� x,�� i�1

�

�i� i�i 1�� x�u�� ix�

g�� x,�� i�1

�

�i� i�i 1�� x � 1�u��1 � ��ix � 1 � �i��.

So the difference, f�( x,�) g�( x,�), can be broken down into twocomponents:

i�1

�

�i� i�i 1x��u�� ix� � u��1 � ��ix � 1 � �i��

� i�1

�

�i� i�i 1�u��1 � ��ix � 1 � �i��.

Since u is concave and increasing, both series are negative. �Proof of Proposition 3. This Proposition is proved with a

single Lemma.

LEMMA 15. If W� is the solution to the Bellman equation,

W�x� � maxa

��u�a � x� � �1 � a� � �W��x � �1 � ��a��

� �1 � ��W�x�,

then

W� � � ��

1 � ��1 � ��W� � ��

��

1 � ��1 � ��.

Proof of Lemma 15. Confirm that the Bellman equation issatisfied for the candidate function W�:

W� x� ��

1 � ��1 � ��W� � � � �

��

1 � ��1 � ��


� maxa

�

1 � ��1 � ��

�u�a � x� � �1 � a� ��

1 � ��1 � ��

W��x � �1 � ��a� � ��

1 � ��1 � �� max

a

�

1 � ��1 � ��u�a � x� � �1 � a�

� �W��x � �1 � ��a��

� maxa

��u�a � x� � �1 � a�

� �W��x � �1 � ��a�� 1 � ��W� x�.

The first equality follows from the definition of the candidatefunction. The second equality follows from the definition of W.The third equality follows from the definition of W. The fourthequality is derived by rearranging the equation. �

Continuing with the proof of Proposition 3, let

V� xR, xG� ��R

1 � ��G W�xR� � ��R

1 � ��G��

�G

1 � ��R W�xG� � ��G

1 � ��R�and confirm that the candidate function satisfies the Cues Bell-man equation:

V� xR, xG� ��R

1 � ��G W�xR� � ��R

1 � ��G��

�G

1 � ��R W�xG� � ��G

1 � ��R�� W� xR�� R� � W� xG�� G�

� maxaR

�R�u�aR � xR� � �1 � aR�


� �W��xR � �1 � ��aR��R�

� �W� xG��G�� . . . � maxaG

�G�u�aG � xG�

� �1 � aG� � �W� xR��R� � �W��xG � �1

� ��aG��G��

� maxaR

�R�u�aR � xR� � �1 � aR�

� �V��xR � �1 � ��aR, xG�� . . .

� maxaG

�G�u�aG � xG� � �1 � aG�

� �V� xR,�xG � �1 � ��aG��. �

Proof of Proposition 7. Fix u� and such that u(1) u(0) � � u(0) u( 1). This is possible since u is strictly concave. Let � � � �R � 1 �, with � � 0. For sufficiently small �, �xR, xG�� 1,0� is a steady state:

lim�30

W�xR� � ��R

1 � ��G� � W� xR��

�u�0�

1 � �since

u�0�

1 � ��

u� 1� �

1 � �

lim�30

W�xG� � ��G

1 � ��R� � W� xG�� 0� � u�0� �

since u�0� � � u�1�.

A cue-management decision to permanently set the cue GREEN(starting from steady state �xR, xG� � �1,0�) yields future payoffsof (u(0) � )/(1 �). And lim�30 V( xR, xG) � u(0)/(1 �). Thisproves the main claim of the proposition.

The final claim in Proposition 7 can be shown by noting thatof the four possible steady states, (�xR, xG� � {�0,0�, �1,0�, �0,1�,�1,1�}), the consumer gains nothing by controlling the cue processwhen she is in either the first or last steady state. WLOG assumethat the consumer is in steady state �1,0�. The best cue-manage-ment decision that the consumer can take is to permanently setthe cue GREEN. This yields a change in welfare of


u�0� �

1 � �� V�1,0�

�u�0� �

1 � ��

�R

1 � ��G W�xR� � ��R

1 � ��G��

�G

1 � ��R W�xG� � ��G

1 � ��R��

u�0� �

1 � ��

�Ru�1 � � � �1 � �R��u�0� � �

1 � �

��R�u�0� � � u�1 � ��

1 � ��

1 � �.

The last inequality follows from the fact that u(0) � u(1 ) � 0 (which is a necessary condition for existence of the �1,0�steady state), and u(0) � u(1 ) (which follows from monoto-nicity of u, and 0 � � 1). �

DEPARTMENT OF ECONOMICS,HARVARD UNIVERSITY

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